The Off-Broadway theatre has also announced the return of A Child's Christmas in Wales adapted and directed by Charlotte Moore.
Kevin P. Hill will direct and choreograph with music direction by Dan Rodriguez.
Gabriella Enriquez, Pablo Torres, Eric Ulloa, and more star in the Andrew Lloyd Webber-Tim Rice musical.
Bender will succeed Patrick Parker, who held the position for nearly three decades.
The Hangmen and The Cripple of Inishmaan playwright recently spoke about shifting out away from theatre in favor of writing for the screen.
Full casting has been announced for the gala presentation of the Jason Robert Brown musical starring Ben Platt and Micaela Diamond.
The writer's body of work also includes One Night... and Zooman and the Sign.
The Broadway favorite will succeed Jefferson Mays as Mayor Shinn later this month.